Definition df-im 15178

Description: Define a function whose value is the imaginary part of a complex number. See imval 15184 for its value, imcli 15245 for its closure, and replim 15193 for its use in decomposing a complex number. (Contributed by NM, 9-May-1999.)

Assertion

Ref	Expression
df-im	⊢ ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))

Detailed syntax breakdown of Definition df-im

Step	Hyp	Ref	Expression
1		cim 15175	. 2 class ℑ
2		vx	. . 3 setvar 𝑥
3		cc 11116	. . 3 class ℂ
4	2	cv 1569	. . . . 5 class 𝑥
5		ci 11120	. . . . 5 class i
6		cdiv 11889	. . . . 5 class /
7	4, 5, 6	co 7423	. . . 4 class (𝑥 / i)
8		cre 15174	. . . 4 class ℜ
9	7, 8	cfv 6543	. . 3 class (ℜ‘(𝑥 / i))
10	2, 3, 9	cmpt 5197	. 2 class (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))
11	1, 10	wceq 1570	1 wff ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))

This definition is used by:  imval  15184  imf  15190  cnre2csqima  34325